Task Sets: Recognize and represent proportional relationships between quantities - Common Core Math - Grade 7

Recall / Warm-Up

Which table shows a proportional relationship between $x$ and $y$ ?

$x$	$y$	$y/x$
2	6	3
4	12	3
6	18	3

$x$	$y$	$y/x$
1	5	5
3	9	3
5	15	3

$x$	$y$	$y/x$
2	7	3.5
4	10	2.5
6	13	2.17

$x$	$y$	$y/x$
0	4	—
2	6	3
4	8	2

A map scale is 1 inch = 25 miles. How many miles does 3 inches represent?

$28$

$75$

$8\frac{1}{3}$

$225$

In a proportional relationship, $y = 9$ when $x = 3$ . What is $y$ when $x = 7$ ? Express as a whole number or fraction.

Fluency Practice

A table shows the relationship between $x$ and $y$ :

$x$	$y$
3	15
6	30
9	45
12	60

Which conclusion is correct?

The relationship is proportional because $y/x = 5$ for the first row, so $k = 5$ .

The relationship is proportional because $y/x = 5$ for every row, confirming a constant ratio.

The relationship is not proportional because the $y$ -values are multiples of 15.

The relationship is proportional because all $y$ -values are larger than $x$ -values.

A proportional relationship is shown in the table:

Pounds of apples ( $x$ )	Total cost in dollars ( $y$ )
2	5
5	12.5
8	20

What is the constant of proportionality $k$ ? Express as a decimal.

A baker uses flour and sugar in a proportional relationship with constant of proportionality $k = \frac{2}{3}$ (cups of sugar per cup of flour). How many cups of sugar does the baker need for 12 cups of flour?

A factory produces widgets at a constant rate: 240 widgets in 4 hours. Write the equation relating widgets $w$ and hours $h$ , then find $w$ when $h = 7$ .

Gas costs $3.50$ per gallon. Let $c$ be the total cost in dollars and $g$ be the number of gallons. Which equation correctly represents this proportional relationship?

$c = \dfrac{g}{3.50}$

$c = g + 3.50$

$c = 3.50g$

$c = 3.50 + g$

Proportional Relationships — Tables, Graphs, Equations, and Verbal Descriptions

Recall / Warm-Up

Fluency Practice